Question: Question 4

The XYZ company is trying to decide whether to market a new product. There is some uncertainty about whether the new product will “catch on” in the marketplace. XYZ management recognizes that it might be prudent to introduce the product in a test market before national introduction and thus its first decision is whether to test market. The fixed cost of the test market is estimated to be $3 million. After getting the results of the test market, XYZ can decide whether to market nationally. Marketing nationally will involve fixed costs of $90 million.

If the initial decision is not to test market, the product can still be introduced on a national basis without a test market. The contribution margin for the product in question is $18 per unit.

XYZ classifies the results in either the test or national market as good, fair or poor. Each of these outcomes is accompanied by a forecast of units sold. These sales volumes (in thousands of units sold) are 200, 100 or 30 in the test market and 6000, 3000 and 900 in the national market (for each of the outcomes of good, fair and poor respectively). Based on previous test markets for similar products, XYZ estimates the probabilities of good, fair, or poor performance to be 0.5, 0.3 and 0.2, respectively, in either the test market or the national market.

If the test market outcome is good, then the probabilities for the national market outcomes are estimated to be 0.80, 0.12 and 0.08. If the test market is fair, these probabilities are 0.20, 0.60 and 0.20 and if the test outcome is poor, the probabilities are 0.20, 0.30 and 0.50.

a) Draw the decision tree (or use Tree Plan to produce the tree) and determine the best course of action assuming that XYZ wishes to maximize EMV.

b) Assume for a moment that we do not have the option to test market but must simply decide whether or not to market nationally. Under this circumstance, calculate the expected value of perfect information (EVPI). In other words, what is the maximum that you would pay a “market clairvoyant” to tell you with certainty whether the introduction will meet a good, fair or poor outcome?

Utility assessment is a tedious process made more difficult in a corporate setting because different executives will have difficulty reaching a consensus on what the function should look like. For this reason we often use a class of functions known as “exponential utility functions” (see text). An exponential utility function has only one adjustable parameter and yet seems to capture the concept quite well. The adjustable parameter is called the “risk tolerance” (R or RT) and it is a measure of how much “risk” the decision maker will tolerate. A person with a large value of RT will accept more risk than one who has a lesser RT. XYZ’s executives have debated their RT and have settled on an amount of $30 million.

c) Using the built in exponential utility function in Treeplan and the RT of $30 million, determine the best course of action. Has the decision changed? Explain.

To do this go to a blank cell below the area used by Treeplan and enter the amount 30 in the cell. Now name the cell RT; that is, use the Formulas / Define Name feature in Excel to label your chosen cell RT (or, while the cell is selected, just type RT into the cell reference box in the ‘formula bar’ above column A). Now click on the first decision node in the tree and go to the “Add Ins” tab, then to “Decision tree” – select “Options” and then “Use Exponential Utility Function”.